On the existence of periodic orbits in a class of mechanical hamiltonian systems -an elementary proof

TL;DR

This paper provides an elementary proof demonstrating the existence of periodic orbits with arbitrary periods in certain Hamiltonian systems, offering insights into planetary system formation.

Contribution

It applies differential topology theorems to establish periodic orbit existence in Hamiltonian systems, addressing a longstanding problem in planetary system dynamics.

Findings

Existence of periodic orbits for specified Hamiltonians.

Application of differential topology theorems to dynamical systems.

Implications for understanding planetary system formation.

Abstract

We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a mathematical answer for the long standing problem of existence of Planetary Sistems around stars.